Design of supersonic asymmetric nozzles

Abstract

Problems which are associated with the design of the optimum contours of asymmetric plane nozzles are considered. In [1], in the case of the “minimum possible” length of the lower wall, this problem was solved exactly by the controlled contour method. For greater lengths of the lower wall, this method is inapplicable and it is necessary to use the so-called general method of Lagrange factors [2, 3]. On the basis of this method, the necessary conditions of optimality of the configurations proposed (but not investigated) in [1] are obtained below, a solution which contains a section of the two-sided extremum is constructed, and configurations which do not contain this section are analyzed. The specifics of the problem considered lead to situations which are different from those encountered earlier in the variational problems of supersonic gasdynamics. The latter is associated both with the specail features of formulation of the combined problem for determining the Lagrange factors and with the disposition of the lines of discontinuity of these factors. In the concluding part of the paper, which is a continuation of [4], the effect of the intensity of the compression wave on the thrust of a “ shortened” asymmetric nozzle is investigated. It is shown that the substitution of the centered wave by a compression wave of very moderate intensity significantly reduces the thrust of the nozzle.